February 10, 2010

As a society, we reward people for making predictions about things that we find interesting to contemplate: Colts or Saints? Will the stock market go up or down tomorrow? Not surprisingly, we don't much punish people for being wrong about their predictions in these nearly random situations that so intrigue us.

Unf0rtunately, that lack of accountability extends to systems that aren't at all as smooth-operating as the NFL playoffs, the systems that we find boring and depressing to think about. So, we allow magical thinking to run amok. For example, a few years ago the Gates Foundation pressured the gigantic Los Angeles Unified School District into making it a requirement for graduating from high school that students pass Algebra I, Geometry, and Algebra II, a course so far over the cognitive capabilities and needs of a large fraction of perfectly nice kids who deserve to go through life as high school graduates that they might as well get a letter from Bill Gates telling them to drop out now and beat the rush.

The notion that students who haven't mastered fractions yet should be taking algebra is the kind of idea that can flourish only in areas of society that are deeply crippled by taboos.

Spurred by a succession of reports pointing to the importance of algebra as a gateway to college, educators and policymakers embraced “algebra for all” policies in the 1990s and began working to ensure that students take the subject by 9th grade or earlier.

A trickle of studies suggests that in practice, though, getting all students past the algebra hump has proved difficult and has failed, some of the time, to yield the kinds of payoffs educators seek.

Among the newer findings:

• An analysis using longitudinal statewide data on students in Arkansas and Texas found that, for the lowest-scoring 8th graders, even making it one course past Algebra 2 might not be enough to help them become “college and career ready” by the end of high school.

• An evaluation of the Chicago public schools’ efforts to boost algebra coursetaking found that, although more students completed the course by 9th grade as a result of the policy, failure rates increased, grades dropped slightly, test scores did not improve, and students were no more likely to attend college when they left the system.

• A 2008 paper by the Brookings Institution suggested that as many as 120,000 students nationwide were “misplaced” in algebra programs, meaning they had test scores on national exams that put them about seven grades below their peers in algebra classes. Further, it said, states with a high proportion of students taking algebra in 8th grade didn’t necessarily outperform other states on national math assessments.

“Simply sticking students in courses without preparing them ahead of time for the class does not seem to work as an intervention,” said Chrys Dougherty, the author of the Arkansas and Texas analysis, published last month by the National Center for Educational Achievement, in Austin, which is owned by the test publisher ACT Inc. “It seems to work with adequately prepared students, but not for the most challenged students.” ...

What Mr. Schmidt found was that the learning gains were greatest for students who moved from either a general math class or a prealgebra class into a full-blown algebra class.

His findings are in keeping with a larger body of studies from the 1990s and early 2000s that suggested algebra was, for many students, the primary gateway to advanced-level mathematics and college. The problem was that too many students—particularly those who were poor or members of disadvantaged minority groups—were turned away at the gate, screened out by ability-grouping practices at their schools. ...

“For the high-achieving kids, there was a big change in the classroom composition, so that changes the quality of classes,” said study co-author Elaine M. Allensworth, the interim co-executive director at the consortium, an independent research group based at the University of Chicago. “That means you have to have teachers who can teach to all classes, and it also means you don’t have an elite group of students who may be getting better advising in smaller classes.”

Can't have that! What elite groups of students who get better advising ever contributed to humanity?

“Meanwhile, the kids who weren’t taking advanced classes before are taking them now,” she said, “but they’re not very engaged in them. They have high absence rates and low levels of learning.”

As the trends became evident, the school system in 2003 began requiring 9th graders who scored below the national median on standardized math tests in 8th grade to take an algebra “support” class in addition to a regular algebra class. Students who scored higher continued to take a single period of algebra.

For the Chicago consortium’s study, the researchers compared outcomes for students just above and below the cutoff for the “double dose” classes.

Worried about the potential for reintroducing tracking, the district also provided professional-development workshops and other resources to the teachers of the support classes, according to Ms. Allensworth.

“Because teachers had more time and resources, the instructional quality in those classes improved quite a bit,” she said. “But the classes ended up concentrating more students with attendance and behavioral problems.”

In the end, the study found, failure rates increased for both the targeted students and for their peers in single-period algebra classes. On the other hand, algebra test scores rose substantially for the students in the double-dose classes.

“The district thought [the double-dose initiative] was a failure because it did not improve pass rates, but our analysis showed that test scores improved a lot,” Ms. Allensworth said.

Part of the problem, the Chicago researcher said, is that schools have little guidance on how to structure algebra programs to serve all students.

Because it's hard to do. It's easier to teach tracked classes, but that's out of fashion ... unless you call them AP classes. Then they are the height of fashion.

Tom Loveless, the author of the report from the Washington-based Brookings Institution on “misplaced” math students in algebra, said the issue is even more complex.

“No one has figured out how to teach algebra to kids who are seven or eight years behind before they get to algebra, and teach it all in one year,” said Mr. Loveless, who favors interventions for struggling students at even earlier ages.

Giving the dumb kids more time to learn the times tables by rote would be a good idea for a start.

Nationwide, research findings may diverge because testing content varies—the TIMSS test has more algebra content than many state exams taken by 8th graders—and because course content varies from classroom to classroom.

“If you take what’s called algebra class, and you look at the actual distribution of allocated time, you find that many of those teachers spend a very large portion of that year on basic arithmetic,” said Mr. Schmidt, who is a distinguished university professor of education at Michigan State’s East Lansing campus. His research on U.S. classrooms has found, in fact, that nearly a third of students studying algebra are using arithmetic books in their classes.

45 comments:

I lived in an eastern European country until the 6th grade, and let me tell you, the math curriculum there was insanely hard by American standards, both in the speed we learned the topic and the difficulty of the problems. Algebra II honors, which I took as a sophomore not that long ago, was a joke compared to the math being taught in my country at that level in a student's academic career. Yet most kids were very well able to keep up, dropping out of school is almost unheard of in the old country. Human potential, I guess.

But an anecdote - last night I was sitting at the dinner table [with a couple of university professors in my family] when a news story about public education was being discussed, and I told them that it was all meaningless anyway because you need an IQ of at least 90 just to be able to read comic books, and blacks and hispanics have average IQs at least 10 points lower than that.

Giving the dumb kids more time to learn the times tables by rote would be a good idea for a start.

Oh boy, here we go again.

You probably need an IQ of 90 to understand addition, and an IQ well into the mid-90s to understand multiplication [at even the most rudimentary level].

With the caveat that I am NOT an accredited expert in the education of low-IQ children, my guess is that children with IQs in the 80s might be able to memorize the the multiplication tables, but that [like Pavlov's dog] they wouldn't understand what it was that they were being required to memorize.

And when you get down into 70s-ish IQs, I doubt that the children are even capable of the rote memorization.

So by my back-of-the-envelope calculation, about half of all black and hispanic kids can't even do the memorizing.

I hail from an Eastern European country as well, but I would caution against making broad generalizations from experience of students who went to school in a good neighborhood. The Communists had a unified national curriculum, sort of like what Gates is trying to pull off, but in practice there was lots of corruption in neighborhoods with dumber kids. Basically, there were no standardized tests back then and the folks testing you for compliance with the curriculum were either your teachers or their immediate colleagues/supervisors. Such had nothing to gain and everything to lose from being overly objective in figuring out just how well they taught geometry to the future bus drivers and similar. So the rumors of working class people in Eastern Europe being great at math, IMHO, are strongly exaggerated. They just didn't have the internet and the dissident people like Steve to do the "na na" over it. As for the better neighborhoods and the smarter students - absolutely, the curriculum and the quality of teaching were often quite stellar.

I live in the DC area and know a lot of people who work for NGOs. Gates gives a lot of money that does a lot of practical good in some parts of the world to reduce malaria, TB, improve diets (that improves IQ) etc. Simple things that really help.

Then his foundation comes up with things like this...if he wanted to do some actual good in this area, he would help these kids find out what they're interested in and what practical job skills they do have, and fund their training in those areas. If he does find inner city kids who have the talent and interest in becoming engineers, pay for them to be put into classrooms away from the disruptors. If he finds future mechanics, fund classes on that.

Then his foundation comes up with things like this...if he wanted to do some actual good in this area, he would help these kids find out what they're interested in and what practical job skills they do have, and fund their training in those areas.

If I might be allowed to beat this dead horse just one more time - you need an IQ well into the 80s to be capable of showing up sober for work every day, reliably & punctually, for your job as a janitor.

Which means that most of these kids have no "practical job skills" whatsoever.

Then his foundation comes up with things like this...if he wanted to do some actual good in this area, he would help these kids find out what they're interested in and what practical job skills they do have, and fund their training in those areas. If he does find inner city kids who have the talent and interest in becoming engineers, pay for them to be put into classrooms away from the disruptors. If he finds future mechanics, fund classes on that."

Or if they have an aptitude for robbery, assault, and murder, support that:

http://www.komonews.com/news/local/9034432.html

As for you aspiring white hoodlums however, sorry, you're out of luck. Whites need not apply for the Bill and Melinda Gates Foundation Scholarships - they aren't eligible.

I attended primary school in Asia and when I returned to the US, I was astounded by the lack of mathematical aptitude of American HS students. I was a mediocre student in Asia, but the top student in all my classes at a SWPL prep school where the average score SAT was 1250.

In Asia, kids are drilled non-stop on the fundamentals of math, algebra, and geometry. We did 3-4hrs of math homework a day.

Sure, Asians have higher visual-spatial IQ on average, but there isn't THAT much of a difference.

Americans these days spend too much time playing sports and being "well rounded". What they really need to do is hit the books. Even the poor ones and dumb ones need to be forced to do lots of repetitive math. It is the only way to learn.

In America you have to be fairly smart to be a CPA. In Asia, accountants are the dumb people. Why? Because everyone received a rigorous education in basic arithmetic and algebra.

Even all those arrogant, urban "creative class" types who consider themselves to be brilliant with sky high IQs can't solve those proverbial "2 trains leave at the same time from 2 different cities at different speeds" questions.

Gates gives a lot of money that does a lot of practical good in some parts of the world to reduce malaria, TB, improve diets (that improves IQ) etc.

Gates could do a little justice and hand back some of the money he overcharged to buyers of that crap called "Windows". On top he could reimburse us all for holding down IT development through his monopoly and thus damaging our economic growth. What really sucks about Gates is that he tries to sell himself as a type of missionary using loot.

Anon asserts that "You probably need an IQ of 90 to understand addition, and an IQ well into the mid-90s to understand multiplication ..."

Well, last year I had to try and explain to a primary school teacher about interest on loans. She interrupts me saying, "I understand that but it's just not fair". Hate to think what she taught the kids.

But, then, I coach a 17 year old in advanced math. He tells me that he's got a new teacher who repeatedly ends up in confusion and has to go over the work again.

Maybe math is just too complicated for most teachers, not to mention kids?

"I live in the DC area and know a lot of people who work for NGOs. Gates gives a lot of money that does a lot of practical good in some parts of the world to reduce malaria, TB, improve diets (that improves IQ) etc. Simple things that really help."

Why do so many posters on this blog make absurd claims about what level of IQ is supposedly "needed" for various trivial things like arithmetic and showing up to work? What world do you freaks live in?

The major urban educational problem is not IQ; it is attendance. You cannot teach students who appear in class only if they have nothing better to do.

If we measured city schools by the achievement of students with, say, 95% attendance records (1 day a month absence or less), those schools would not be nearly as far behind suburban and rural schools as they appear to be now.

I propose that every high school student be required to pass courses in nuclear physics. After all, nuclear engineers are among the private sector's reasonably high-earners.

Many of the kids won't go in that career direction, but some will, and the others will be enriched by the experience.

Also mandatory calculus. And mandatory Goethe in the original German.

Someone tell Bill Gates. He is interested in untapped talent. (Remember his search for the African Einstein?) Of course, a genuine search for talent among the lower classes - by administering IQ tests - is verboten, a Very Bad Idea that neither Bill nor Melinda would be caught dead entertaining.

In Mission to Mars Val Kilmer's character figures out which way to go find the spacecraft. He says "Mrs. Jones my teacher always said that one day algebra would save my life".

Anecdote #2

When I taught undergraduate statistics I used to give the class an algebra problem that I picked up from a TV show. No one ever was able to solve it. The show was The Smurfs.

Anecdote #3

Today my home town Washington D.C. is buried under a blizzard. Yet the government threatens to cripple the already faltering economy with remedies for the imagined Anthropogenic Global Warming. The AGW bandwagon really started to roll with infamous hockey stick graph. The image of the hockey stick still burns in the public mind. Yet anyone who is not innumerate can easily look up the formula for Principal Components Analysis in Wikipedia and see at once that Michael Mann didn't use the right formula. This is what McIntyre and Wegman tried to explain in words. Anyone who has even a little algebra can see this for themselves.

Anecdote #4

Bill Gates is not a normal CEO. He is for example good at algebra. Before he semi-retired he used to challenge any of his programmers to write any program in any language and he would beat them writing in BASIC.

Anecdote #5

I had trouble learning the multiplication tables when I was a kid. All that rote memorization was difficult for me. So I developed a simple series of algorithms that allowed me to calculate the right answer. For example nine times five is five times ten (just add a zero) minus five. I always got the right answer but it wasn't fast. My parents hired a math tutor who discouraged all this foolish calculation and drilled me in memorization.

He owns the land (the dominant Windows OS) that a majority of the world lives on doing all their work, going about their lives, etc while paying rent to the landowner. The landowner in return does minimal, half-assed, shoddy maintenance and land upkeep and tries to keep his tenants from leaving or moving off his land.

I propose a simple remedy: we can require algebra 2 for high school graduation, but to prepare teachers for this, we should first require a differential equations course for graduation with an education degree.

What about the experience of Jaime Escalante? This post jogged my memory of the movie I saw about this guy teaching poor kids calculus about 20 years ago.

I have said repeatedly that if a researcher really cared about this crisis, then such a researcher would seek out Escalante's former students and establish who they were then [when they received Escalante's instruction] and what they are doing with their lives now [a quarter century later]:

1) Were they primarily mestizo Hispanics [with a great deal of Mexican Indian blood in them], or were they "Castilian/Hapsburgian" Caucasian Hispanics, or were they Koreans or Vietnamese or Chinese or what?

2) Once you correct for their race [as in 1)], and especially once you correct for their IQs, then how do their long term career experiences compare to control sets of children from that era, with similar backgrounds and similar IQs, who did not receive Escalante's instruction?

In particular, 2) would go a long way towards answering the "Pavlovian Dog" criticism which was leveled against Escalante's students.

i don't think that was Gates, though he's done some things that suggest he's going in that direction. There's no one goofier than brilliant white liberal do gooders.No, the brilliant white man who went in search of a hypothetical brilliant black African must be other than the wheelchair bound Steven Hawkins. I presume.

I spent some time at Jaime Escalante's old school, Garfield High, as part of my teacher training. It's a huge school, over 5000 kids, 98% Hispanic. They claim a dropout rate of 22%, but since there are over 1800 9th graders and only 600+ 12th graders, they're lying. When you count how many pass the exit exam, (CAHSEE), they actually graduate about 10% of the entering freshmen. That's the reality of the place. I was told by some of the older teachers that Escalante's students were the pick of the litter, not a gang kid among them. So, out of 1800 plus entering students, at the end of four years, 30 or 40 are capable of beginning calculus. Around two percent.

I was told by some of the older teachers that Escalante's students were the pick of the litter, not a gang kid among them. So, out of 1800 plus entering students, at the end of four years, 30 or 40 are capable of beginning calculus. Around two percent.

What was your sense of their ethnicities?

Also, did any of Escalante's kids make it in technical work?

Are any of them now working as engineers or computer programmers or draftsmen?

[Although obviously that's gonna be a very difficulty question to answer, since it won't be easy to separate the real workers from the quota hires.]

Btw, being conscientious and showing up to work on time does not require any particular IQ.

I met many of my grandmother's former students -- she taught special education in middle school in South Carolina. They could read at a very basic level and could do some basic arithmetic [addition, subtraction].

Their jobs were on the order of sweeping up factories or raking leaves - something very repetitive. They were excellent workers at the tasks they were given.

Plenty of high IQ ne'er-do-wells, and plenty of conscientious low IQ people. You need to understand the difference between the Big Five personality factors [neuroticism, openness to experience, extraversion, conscientiousness, agreeableness] and IQ -- yes, a couple of these traits have some correlation to IQ, but it's not 1 or -1.

Btw, being conscientious and showing up to work on time does not require any particular IQ.

Do you honestly believe, in your heart of hearts, that IQ does not correlate well with things like sobriety, punctuality, hygiene, grooming, or the [reliable] capacity to regularly launder and iron one's work clothes?

IQ certainly correlates with the kinds of overweight, obesity, grotesque obesity, morbid obesity, and "so-damned-fat that the fire department has to come to your house and cut a hole in the wall so as to get your blubber-ass to the hospital" self-induced handicaps which render even the least-skilled job openings useless to low-IQ people.

Indeed, he (and we) would be better off pushing for a more meritocratic education system back home in the UK. Something all our main parties, in their infinite wisdom, have made clear they are steadfastly against.

He owns the land (the dominant Windows OS) that a majority of the world lives on doing all their work, going about their lives, etc while paying rent to the landowner. The landowner in return does minimal, half-assed, shoddy maintenance and land upkeep and tries to keep his tenants from leaving or moving off his land

Nicely put, thats the James Bowery position I believe, but you put it in terms I can get a grip on better.

being conscientious and showing up to work on time does not require any particular IQ.

I met many of my grandmother's former students -- she taught special education in middle school in South Carolina. They could read at a very basic level and could do some basic arithmetic [addition, subtraction].

Their jobs were on the order of sweeping up factories or raking leaves - something very repetitive. They were excellent workers at the tasks they were given.

And if they were your grandmother's students in South Carolina, they were physically disciplined definitely at home and possibly by her, and held to the straight and narrow by the tone of the culture around them even after they got too old to spank.

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